
<!DOCTYPE html>
<html>

	<head>
	<title>CAIJL's Blog</title>
	<meta charset="utf-8"/>
	<link rel="stylesheet" href="/font-awesome-4.7.0/css/font-awesome.min.css">

	<link rel="stylesheet" href="/bootstrap-3.3.7/css/bootstrap.min.css">
	<script src="/jquery-2.1.1/jquery.min.js"></script>
	<script src="/bootstrap-3.3.7/js/bootstrap.min.js"></script>

	<link rel="stylesheet" href="/css/bootstrap-slider.min.css">
	<script src="/js/bootstrap-slider.min.js"></script>
	
	<link rel="stylesheet" href="/css/main.css">
	<script src="/js/main.js"></script>
	
	<link rel="stylesheet" href="/css/cursor.css">
	<script src="/js/cursor.js"></script>
	
	
	<link rel="stylesheet" href="/css/code.css">
	<!--link rel="stylesheet" href="/css/markdown.css"-->
	
	<link rel="stylesheet" href="/css/head.css">

	<script src="/js/window.js"></script>
	<script src='//unpkg.com/valine/dist/Valine.min.js'></script>
	</head>
<body>

	<link rel="stylesheet" href="/katex/katex.min.css" crossorigin="anonymous">
	<script src="/katex/katex.min.js" crossorigin="anonymous"></script>
	<script src="/katex/contrib/mathtex-script-type.min.js" defer></script>
	<script defer src="/katex/contrib/auto-render.min.js"crossorigin="anonymous"
	    onload="renderMathInElement(document.body);"></script>
	<script>document.addEventListener("DOMContentLoaded", function() {renderMathInElement(document.body,{"delimiters":[{left: "$", right: "$", display: false}]});});</script>
	<nav class="navbar navbar-default header card" role="navigation" style="width: 100%;">
	<div class="container-fluid"> 
	<div class="navbar-header">
		<button type="button" class="navbar-toggle" data-toggle="collapse"
				data-target="#example-navbar-collapse">
			<span class="icon-bar"></span>
			<span class="icon-bar"></span>
			<span class="icon-bar"></span>
		</button>
		<a class="navbar-brand" href="/"><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">C</mi><mi mathvariant="bold">A</mi><mi mathvariant="bold">I</mi><mi mathvariant="bold">J</mi><msup><mi mathvariant="bold">L</mi><mo mathvariant="bold" lspace="0em" rspace="0em">′</mo></msup><mi mathvariant="bold">s</mi><mi mathvariant="bold">B</mi><mi mathvariant="bold">L</mi><mi mathvariant="bold">O</mi><mi mathvariant="bold">G</mi></mrow><annotation encoding="application/x-tex">\mathbf{CAIJL'sBLOG}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.751892em; vertical-align: 0em;"></span><span class="mord"><span class="mord mathbf">C</span><span class="mord mathbf">A</span><span class="mord mathbf">I</span><span class="mord mathbf">J</span><span class="mord"><span class="mord mathbf">L</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.751892em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathbf">s</span><span class="mord mathbf">B</span><span class="mord mathbf">L</span><span class="mord mathbf">O</span><span class="mord mathbf">G</span></span></span></span></span></span></a>
	</div>
	<div class="collapse navbar-collapse" id="example-navbar-collapse">
		<ul class="nav navbar-nav" style="background-color:#fcfcfc">
			<li><a href="/"><i class="menu-item-icon fa fa-fw fa-home"></i>首页</a></li>
			<li><a href="/archives/"><i class="menu-item-icon fa fa-fw fa-archive"></i>文章</a></li>
			<li><a href="/tags/"><i class="menu-item-icon fa fa-fw fa-tags"></i>标签</a></li>
			<li><a href="/settings/"><i class="menu-item-icon fa fa-fw fa-cogs"></i>设置</a></li>
			<!--li><a href="/about/"><i class="menu-item-icon fa fa-fw fa-user"></i>关于</a></li-->
			<li><a href="/games/"><i class="menu-item-icon fa fa-fw fa-gamepad"></i>其它</a></li>
			

		</ul>
	</div>
	</div>
	</nav>
<div class="container">
	<div style="height: 60px;"></div>
	<div class="row" >
		<div class="col-md-8">
			<div class="panel panel-default card" style="padding: 10px;position: relative;">
                <img src='/img/bg/19.png' style="width:100%"/>
				<span style="position: absolute;left:15px;bottom:15px;width:90%;"><font class="view-text" style="color:#fcfcfc;font-size:25px">题解 P3312 【[SDOI2014]数表】</font><br><a href="/tags/2020/" class="tag"><span  style="background-color: rgb(52, 152, 219);">2020</span></a>&nbsp;<a href="/tags/莫比乌斯反演/" class="tag"><span  style="background-color: rgb(231, 76, 60);">莫比乌斯反演</span></a>&nbsp;<a href="/tags/树状数组/" class="tag"><span  style="background-color: rgb(231, 76, 60);">树状数组</span></a>&nbsp;<a href="/tags/题解/" class="tag"><span  style="background-color: rgb(82, 196, 26);">题解</span></a></span>
			</div>
			<div class="panel panel-default card" style="padding: 10px;" id="main">
                <h1 id="duliu">一道数论+数据结构的DuLiu题</h1>
<p>我们要求的就是
<script type="math/tex; mode=display">Ans=\sum_{i=1}^n\sum_{j=1}^m\sum_{d|i\wedge d|j}d[\sum_{d|i\wedge d|j}d\leq a]</script>
考虑到<script type="math/tex">d|i \wedge d|j</script>等价于<script type="math/tex"> d|gcd(i,j)</script>
<script type="math/tex; mode=display">Ans=\sum_{i=1}^n\sum_{j=1}^m\sum_{d|gcd(i,j)}d[\sum_{d|gcd(i,j)}d\leq a]</script>
</p>
<!--more-->
<p>令<script type="math/tex">f(x)=\sum_{i|x}i</script>,即因子和,
把<script type="math/tex">f(x)</script>带入
<script type="math/tex; mode=display">Ans=\sum_{i=1}^n\sum_{j=1}^m f(gcd(i,j))[f(gcd(i,j))\leq a]</script>
<script type="math/tex; mode=display">枚举因数</script>
<script type="math/tex; mode=display">Ans=\sum_{d=1}^n \sum_{i=1}^{\lfloor\frac n d\rfloor}\sum_{j=1}^{\lfloor\frac m d\rfloor} f(d)[f(d)\leq a][gcd(i,j)==1]</script>
把<script type="math/tex">f(d)[f(d)\leq a]</script>提前并使用莫比乌斯反演
<script type="math/tex; mode=display">Ans=\sum_{d=1}^n f(d)[f(d)\leq a]\sum_{i=1}^{\lfloor\frac n d\rfloor}\sum_{j=1}^{\lfloor\frac m d\rfloor} \sum_{x|gcd(i,j)} \mu(x)</script>
<script type="math/tex; mode=display">把枚举x提前</script>
<script type="math/tex; mode=display">Ans=\sum_{d=1}^n f(d)[f(d)\leq a]\sum_{x=1}^{\lfloor \frac n d \rfloor} \mu(x)\sum_{i=1}^{\lfloor\frac n d\rfloor}[x|i]\sum_{j=1}^{\lfloor\frac m d\rfloor}[x|j] </script>
<script type="math/tex; mode=display">稍稍化简</script>
<script type="math/tex; mode=display">Ans=\sum_{d=1}^n f(d)[f(d)\leq a]\sum_{x=1}^{\lfloor \frac n d \rfloor} \mu(x)\lfloor \frac n {dx}\rfloor \lfloor \frac m {dx}\rfloor </script>
<script type="math/tex; mode=display">令dx=T</script>
<script type="math/tex; mode=display">Ans=\sum_{T=1}^n\sum_{d|T} f(d)[f(d)\leq a]\mu(\frac T d)\lfloor \frac n T\rfloor \lfloor \frac m T\rfloor </script>
我们发现，只有<script type="math/tex">f(d)\leq a</script>的<script type="math/tex">d</script>,才能对<script type="math/tex">ans</script>有贡献
辣么如果从<script type="math/tex">a\to a'</script>,<script type="math/tex">A=\{x,a<f(x)\leq a'\}</script>,会对<script type="math/tex">A</script>中所有元素及其倍数造成贡献
因此我们可以用某种数据结构来维护<script type="math/tex">\sum_{d|T} f(d)[f(d)\leq a]\mu(\frac T d)</script>,很明显BIT是一种很好的选择
<div class="highlight"><pre><span></span><code><span class="linenos" data-linenos=" 1 "></span><span class="cp">#include</span><span class="cpf">&lt;bits/stdc++.h&gt;</span><span class="cp"></span>
<span class="linenos" data-linenos=" 2 "></span><span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span><span class="p">;</span>
<span class="linenos" data-linenos=" 3 "></span><span class="k">const</span> <span class="kt">int</span> <span class="n">maxn</span><span class="o">=</span><span class="mf">1e5</span><span class="o">+</span><span class="mi">10</span><span class="p">;</span>
<span class="linenos" data-linenos=" 4 "></span><span class="k">template</span> <span class="o">&lt;</span><span class="k">class</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span> <span class="o">&amp;</span><span class="n">x</span><span class="p">){</span>
<span class="linenos" data-linenos=" 5 "></span>    <span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">char</span> <span class="n">c</span><span class="o">=</span><span class="n">getchar</span><span class="p">();</span>
<span class="linenos" data-linenos=" 6 "></span>    <span class="k">for</span><span class="p">(;</span><span class="o">!</span><span class="n">isdigit</span><span class="p">(</span><span class="n">c</span><span class="p">);</span><span class="n">c</span><span class="o">=</span><span class="n">getchar</span><span class="p">());</span>
<span class="linenos" data-linenos=" 7 "></span>    <span class="k">for</span><span class="p">(;</span><span class="n">isdigit</span><span class="p">(</span><span class="n">c</span><span class="p">);</span><span class="n">c</span><span class="o">=</span><span class="n">getchar</span><span class="p">())</span><span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">*</span><span class="mi">10</span><span class="o">+</span><span class="n">c</span><span class="o">-</span><span class="sc">&#39;0&#39;</span><span class="p">;</span>
<span class="linenos" data-linenos=" 8 "></span>    <span class="k">return</span><span class="p">;</span>
<span class="linenos" data-linenos=" 9 "></span><span class="p">}</span>
<span class="linenos" data-linenos="10 "></span><span class="k">template</span> <span class="o">&lt;</span><span class="k">class</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kt">void</span> <span class="n">write</span><span class="p">(</span><span class="n">T</span> <span class="n">x</span><span class="p">){</span>
<span class="linenos" data-linenos="11 "></span>    <span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">&lt;</span><span class="mi">0</span><span class="p">)</span><span class="n">putchar</span><span class="p">(</span><span class="sc">&#39;-&#39;</span><span class="p">),</span><span class="n">x</span><span class="o">=-</span><span class="n">x</span><span class="p">;</span>
<span class="linenos" data-linenos="12 "></span>    <span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">&gt;=</span><span class="mi">10</span><span class="p">)</span><span class="n">write</span><span class="p">(</span><span class="n">x</span><span class="o">/</span><span class="mi">10</span><span class="p">);</span>
<span class="linenos" data-linenos="13 "></span>    <span class="n">putchar</span><span class="p">(</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="o">+</span><span class="sc">&#39;0&#39;</span><span class="p">);</span>
<span class="linenos" data-linenos="14 "></span><span class="p">}</span>
<span class="linenos" data-linenos="15 "></span><span class="kt">bool</span> <span class="n">isprime</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span>
<span class="linenos" data-linenos="16 "></span><span class="kt">int</span> <span class="n">miu</span><span class="p">[</span><span class="n">maxn</span><span class="p">],</span><span class="n">prime</span><span class="p">[</span><span class="n">maxn</span><span class="p">],</span><span class="n">tot</span><span class="p">;</span>
<span class="linenos" data-linenos="17 "></span><span class="kt">int</span> <span class="n">sigma</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span><span class="c1">//因数和 </span>
<span class="linenos" data-linenos="18 "></span><span class="kt">void</span> <span class="nf">init</span><span class="p">(){</span>
<span class="linenos" data-linenos="19 "></span>    <span class="n">memset</span><span class="p">(</span><span class="n">isprime</span><span class="p">,</span><span class="mh">0xff</span><span class="p">,</span><span class="k">sizeof</span> <span class="n">isprime</span><span class="p">);</span>
<span class="linenos" data-linenos="20 "></span>    <span class="n">tot</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">miu</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="21 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">2</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="22 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">isprime</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="linenos" data-linenos="23 "></span>            <span class="n">prime</span><span class="p">[</span><span class="o">++</span><span class="n">tot</span><span class="p">]</span><span class="o">=</span><span class="n">i</span><span class="p">,</span><span class="n">miu</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos="24 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">j</span><span class="o">&lt;=</span><span class="n">tot</span><span class="o">&amp;&amp;</span><span class="n">i</span><span class="o">*</span><span class="n">prime</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">;</span><span class="n">j</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="25 "></span>            <span class="n">isprime</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">prime</span><span class="p">[</span><span class="n">j</span><span class="p">]]</span><span class="o">=</span><span class="nb">false</span><span class="p">;</span>
<span class="linenos" data-linenos="26 "></span>            <span class="k">if</span><span class="p">(</span><span class="n">i</span><span class="o">%</span><span class="n">prime</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
<span class="linenos" data-linenos="27 "></span>                <span class="n">miu</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">prime</span><span class="p">[</span><span class="n">j</span><span class="p">]]</span><span class="o">=-</span><span class="n">miu</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<span class="linenos" data-linenos="28 "></span>            <span class="k">else</span><span class="p">{</span>
<span class="linenos" data-linenos="29 "></span>                <span class="n">miu</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">prime</span><span class="p">[</span><span class="n">j</span><span class="p">]]</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="30 "></span>                <span class="k">break</span><span class="p">;</span>
<span class="linenos" data-linenos="31 "></span>            <span class="p">}</span>
<span class="linenos" data-linenos="32 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="33 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="34 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="35 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">*</span><span class="n">j</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">;</span><span class="n">j</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="36 "></span>            <span class="n">sigma</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">j</span><span class="p">]</span><span class="o">+=</span><span class="n">i</span><span class="p">;</span>
<span class="linenos" data-linenos="37 "></span><span class="p">}</span>
<span class="linenos" data-linenos="38 "></span><span class="k">struct</span> <span class="nc">BIT</span><span class="p">{</span>
<span class="linenos" data-linenos="39 "></span>    <span class="cp">#define lowbit(x) x&amp;(-x)</span>
<span class="linenos" data-linenos="40 "></span>    <span class="kt">signed</span> <span class="n">tree</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span>
<span class="linenos" data-linenos="41 "></span>    <span class="kt">void</span> <span class="nf">add</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span><span class="p">,</span><span class="kt">int</span> <span class="n">val</span><span class="p">){</span>
<span class="linenos" data-linenos="42 "></span>        <span class="c1">//printf(&quot;A %d %d\n&quot;,x,val);</span>
<span class="linenos" data-linenos="43 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">x</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">){</span>
<span class="linenos" data-linenos="44 "></span>            <span class="n">tree</span><span class="p">[</span><span class="n">x</span><span class="p">]</span><span class="o">+=</span><span class="n">val</span><span class="p">;</span>
<span class="linenos" data-linenos="45 "></span>            <span class="n">x</span><span class="o">+=</span><span class="n">lowbit</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos="46 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="47 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="48 "></span>    <span class="kt">signed</span> <span class="nf">query</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span><span class="p">){</span>
<span class="linenos" data-linenos="49 "></span>        <span class="c1">//printf(&quot;Q %d\n&quot;,x);</span>
<span class="linenos" data-linenos="50 "></span>        <span class="kt">signed</span> <span class="n">ret</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="51 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">x</span><span class="p">){</span>
<span class="linenos" data-linenos="52 "></span>            <span class="n">ret</span><span class="o">+=</span><span class="n">tree</span><span class="p">[</span><span class="n">x</span><span class="p">];</span>
<span class="linenos" data-linenos="53 "></span>            <span class="n">x</span><span class="o">-=</span><span class="n">lowbit</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos="54 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="55 "></span>        <span class="k">return</span> <span class="n">ret</span><span class="p">;</span>
<span class="linenos" data-linenos="56 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="57 "></span><span class="p">}</span><span class="n">A</span><span class="p">;</span>
<span class="linenos" data-linenos="58 "></span><span class="k">struct</span> <span class="nc">Num</span><span class="p">{</span>
<span class="linenos" data-linenos="59 "></span>    <span class="kt">int</span> <span class="n">id</span><span class="p">,</span><span class="n">val</span><span class="p">;</span>
<span class="linenos" data-linenos="60 "></span>    <span class="kt">bool</span> <span class="k">operator</span><span class="o">&lt;</span><span class="p">(</span><span class="k">const</span> <span class="n">Num</span> <span class="n">b</span><span class="p">)</span><span class="k">const</span><span class="p">{</span><span class="k">return</span> <span class="n">val</span><span class="o">&lt;</span><span class="n">b</span><span class="p">.</span><span class="n">val</span><span class="p">;}</span>
<span class="linenos" data-linenos="61 "></span><span class="p">}</span><span class="n">S</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span>
<span class="linenos" data-linenos="62 "></span><span class="k">struct</span> <span class="nc">Que</span><span class="p">{</span>
<span class="linenos" data-linenos="63 "></span>    <span class="kt">int</span> <span class="n">id</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">m</span><span class="p">,</span><span class="n">a</span><span class="p">;</span>
<span class="linenos" data-linenos="64 "></span>    <span class="kt">bool</span> <span class="k">operator</span><span class="o">&lt;</span><span class="p">(</span><span class="k">const</span> <span class="n">Que</span> <span class="n">b</span><span class="p">)</span><span class="k">const</span><span class="p">{</span><span class="k">return</span> <span class="n">a</span><span class="o">&lt;</span><span class="n">b</span><span class="p">.</span><span class="n">a</span><span class="p">;}</span>
<span class="linenos" data-linenos="65 "></span><span class="p">}</span><span class="n">Q</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span>
<span class="linenos" data-linenos="66 "></span><span class="kt">signed</span> <span class="n">ans</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span>
<span class="linenos" data-linenos="67 "></span><span class="kt">int</span> <span class="n">t</span><span class="p">;</span>
<span class="linenos" data-linenos="68 "></span><span class="kt">void</span> <span class="nf">solve</span><span class="p">(){</span>
<span class="linenos" data-linenos="69 "></span>    <span class="kt">int</span> <span class="n">now</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="c1">//已经用过的S </span>
<span class="linenos" data-linenos="70 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">t</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="71 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="n">now</span><span class="o">+</span><span class="mi">1</span><span class="p">].</span><span class="n">val</span><span class="o">&lt;=</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">a</span><span class="o">&amp;&amp;</span><span class="n">now</span><span class="o">+</span><span class="mi">1</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">){</span>
<span class="linenos" data-linenos="72 "></span>            <span class="n">now</span><span class="o">++</span><span class="p">;</span>
<span class="linenos" data-linenos="73 "></span>            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">j</span><span class="o">*</span><span class="n">S</span><span class="p">[</span><span class="n">now</span><span class="p">].</span><span class="n">id</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">;</span><span class="n">j</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="74 "></span>                <span class="n">A</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">j</span><span class="o">*</span><span class="n">S</span><span class="p">[</span><span class="n">now</span><span class="p">].</span><span class="n">id</span><span class="p">,</span><span class="n">miu</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">S</span><span class="p">[</span><span class="n">now</span><span class="p">].</span><span class="n">val</span><span class="p">);</span>
<span class="linenos" data-linenos="75 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="76 "></span>        <span class="n">ans</span><span class="p">[</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">id</span><span class="p">]</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="77 "></span>        <span class="kt">int</span> <span class="n">n</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">m</span><span class="p">,</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">n</span><span class="p">),</span><span class="n">m</span><span class="o">=</span><span class="n">min</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">m</span><span class="p">,</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">n</span><span class="p">);</span>
<span class="linenos" data-linenos="78 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">l</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">r</span><span class="p">;</span><span class="n">l</span><span class="o">&lt;=</span><span class="n">m</span><span class="p">;</span><span class="n">l</span><span class="o">=</span><span class="n">r</span><span class="o">+</span><span class="mi">1</span><span class="p">){</span>
<span class="linenos" data-linenos="79 "></span>            <span class="n">r</span><span class="o">=</span><span class="n">min</span><span class="p">(</span><span class="n">m</span><span class="o">/</span><span class="p">(</span><span class="n">m</span><span class="o">/</span><span class="n">l</span><span class="p">),</span><span class="n">n</span><span class="o">/</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">l</span><span class="p">));</span>
<span class="linenos" data-linenos="80 "></span>            <span class="n">ans</span><span class="p">[</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">id</span><span class="p">]</span><span class="o">+=</span><span class="p">(</span><span class="n">m</span><span class="o">/</span><span class="n">l</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">l</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">A</span><span class="p">.</span><span class="n">query</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="o">-</span><span class="n">A</span><span class="p">.</span><span class="n">query</span><span class="p">(</span><span class="n">l</span><span class="mi">-1</span><span class="p">));</span>
<span class="linenos" data-linenos="81 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="82 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="83 "></span><span class="p">}</span> 
<span class="linenos" data-linenos="84 "></span><span class="kt">signed</span> <span class="nf">main</span><span class="p">(){</span>
<span class="linenos" data-linenos="85 "></span>    <span class="n">init</span><span class="p">();</span>
<span class="linenos" data-linenos="86 "></span>    <span class="n">read</span><span class="p">(</span><span class="n">t</span><span class="p">);</span>
<span class="linenos" data-linenos="87 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;</span><span class="n">maxn</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="88 "></span>        <span class="n">S</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">=</span><span class="p">{</span><span class="n">i</span><span class="p">,</span><span class="n">sigma</span><span class="p">[</span><span class="n">i</span><span class="p">]};</span>
<span class="linenos" data-linenos="89 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">t</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="90 "></span>        <span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">id</span><span class="o">=</span><span class="n">i</span><span class="p">;</span>
<span class="linenos" data-linenos="91 "></span>        <span class="n">read</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">n</span><span class="p">);</span><span class="n">read</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">m</span><span class="p">);</span><span class="n">read</span><span class="p">(</span><span class="n">Q</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">a</span><span class="p">);</span>
<span class="linenos" data-linenos="92 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="93 "></span>    <span class="n">sort</span><span class="p">(</span><span class="n">S</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">S</span><span class="o">+</span><span class="n">maxn</span><span class="p">);</span><span class="n">sort</span><span class="p">(</span><span class="n">Q</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">Q</span><span class="o">+</span><span class="n">t</span><span class="o">+</span><span class="mi">1</span><span class="p">);</span>
<span class="linenos" data-linenos="94 "></span>    <span class="n">solve</span><span class="p">();</span>
<span class="linenos" data-linenos="95 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">t</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="96 "></span>        <span class="n">write</span><span class="p">((</span><span class="mf">1l</span><span class="n">l</span><span class="o">*</span><span class="n">ans</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">+</span><span class="p">(</span><span class="mf">1l</span><span class="n">l</span><span class="o">&lt;&lt;</span><span class="mi">31</span><span class="p">))</span><span class="o">%</span><span class="p">(</span><span class="mf">1l</span><span class="n">l</span><span class="o">&lt;&lt;</span><span class="mi">31</span><span class="p">)),</span><span class="n">putchar</span><span class="p">(</span><span class="sc">&#39;\n&#39;</span><span class="p">);</span>
<span class="linenos" data-linenos="97 "></span><span class="p">}</span>
</code></pre></div></p>
			</div>
			<div class="panel panel-default card" style="padding: 10px;height: 50px;font-size: 20px;">
				<a style="float: left;" href="\article\CF117D.html"><i class="fa fa-angle-double-left"></i></a><a style="float: right;" href="\article\P3172.html"><i class="fa fa-angle-double-right"></i></a>
			</div>
			<div class="panel panel-default card" style="padding: 10px;font-size: 20px;" id="vcomments">
				
			</div>
			<script>
				new Valine({
					el: '#vcomments',
					appId: 'PAlFUPg0pQVTFTEo8gCB4BCf-gzGzoHsz',
					appKey: 'U38ejnLUiizJ6vLyp6ql4hRq',
					path: window.location.pathname
				})
			</script>
		</div>
		<div class="col-md-3">
				<div class="panel panel-default card">
				<div class="panel-heading">
					<h3 class="panel-title">
						<i class="fa fa-info"></i>&emsp;
						<strong>文章信息</strong>
					</h3>
				</div>
                <div style="margin: 10px;">
                    <div style="margin-top: 8px;display: flex;"> 
    <span style="flex: 1 0 auto;margin-right: 6px;">标题</span>
    <span><font style="font-weight: bold">题解 P3312 【[SDOI2014]数表】</font></span>
	</div><div style="margin-top: 8px;display: flex;"> 
    <span style="flex: 1 0 auto;margin-right: 6px;">日期</span>
    <span>2020-06-05 19:01:00</span>
	</div>
                </div>
				</div>
				<div class="panel panel-default card">
				<div class="panel-heading">
					<h3 class="panel-title">
						<i class="fa fa-tag"></i>&emsp;
						<strong>标签</strong>
					</h3>
				</div>
				<div style="margin: 10px;">
					<a href="/tags/2020/" class="tag"><span  style="background-color: rgb(52, 152, 219);">2020</span></a>&nbsp;<a href="/tags/莫比乌斯反演/" class="tag"><span  style="background-color: rgb(231, 76, 60);">莫比乌斯反演</span></a>&nbsp;<a href="/tags/树状数组/" class="tag"><span  style="background-color: rgb(231, 76, 60);">树状数组</span></a>&nbsp;<a href="/tags/题解/" class="tag"><span  style="background-color: rgb(82, 196, 26);">题解</span></a>
				</div>
				</div>
				
			<div class="panel panel-default card">
					<div class="panel-heading">
						<h3 class="panel-title">
							<i class="fa fa-user-circle-o"></i>&emsp;
							<strong>caijicjl</strong>
						</h3>
					</div>
					<div style="width: 60%;display: inline-block;padding-top: 10px;">
						<ul class="propertyLinks" style="list-style-type: none;">
							<li>
								<img style="vertical-align:middle;position:relative;top:-2px" src="/img/rating-16x16.png">
								Rating:&nbsp;
								<span style="font-weight:bold;color: gray ">312</span>
							</li>
							<li>
								<img style="vertical-align:middle;position:relative;top:-2px" src="/img/star_blue_16.png">
								Contribution:&nbsp;
								<span style="color:gray;font-weight:bold;">0</span>
							</li>
						</ul>
						<ul class="nav-links">
							<li><a href="/settings/">Settings</a></li>
							<li><a href="/archives/">Blog</a></li>
							<li><a href="/teams">Teams</a></li>
							<li><a href="/submissions/dingdingsb">Submissions</a></li>
							<li><a href="/usertalk">Talks</a></li>
							<li><a href="/contests/with/dingdingsb">Contests</a></li>
						</ul>
					</div>
					<div style="display:inline-block;vertical-align: top;margin: 10px;text-align: center;">
						<div style="height:50px;width:50px"><img src="/img/avatar.png"/></div>
						<div><a href="https://www.luogu.com.cn/user/174304" style="font-weight:bold;color:gray">caijicjl</a></div>
					</div>
				</div>
		<div class="panel panel-default card">
				<div class="panel-heading">
					<h3 class="panel-title">
						<i class="fa fa-external-link"></i>&emsp;
						<strong>画中画</strong>
					</h3>
				</div>
				<div style="width:100%;margin:10px">
				<input type="text" id="url"/>
				<input value="创建" type="button" onclick="creat('kk')" /> 
				</div>
		</div>
		<script src="/js/hitokoto.js"></script>
							

				
				<span id="kk"></span>
				<div  id="myScrollspy" class="card" style="width: 100%;"  data-spy="affix">
					<script src="/js/make_toc.js"></script>
				</div>
		</div>
	</div>
 </div>
</body>
</html>
